Not my favorite movie but I like this scene:
- As part of his contract, Brando only worked till 4 every day and then he would leave to go see his analyst. Brando’s mother had recently died and the conflicted young actor was in therapy to resolve his issues with his parents. Interestingly, for the film’s classic scene between Rod Steiger and Brando in the back of the cab, all Steiger’s close-ups were filmed after Brando had left for the day, so his lines were read by one of the crew members.
- Most of the solo shots of Rod Steiger during the famous taxicab scene were done after Marlon Brando had left for the day. Steiger was deeply hurt and annoyed at Brando’s apparent rudeness, but used these emotions to add to his performance.
- The line “You don’t understand! I coulda had class. I coulda been a contender. I could’ve been somebody, instead of a bum, which is what I am,” was ranked at number three in the American Film Institute’s top 100 memorable quotes.
More trivia at IMDB:
All Things Cool 
The Godfather Behind the scenes – Marlon Brando